8 papers
A Feynman--Kac representation of a non-conservative and path-dependent nonlinear reaction-diffusion-advection system
Daniela Morale, Leonardo Tarquini, Stefania Ugolini
We provide a probabilistic interpretation of a weakly parabolic PDE--ODE system with a reaction term, which makes the dynamics non-conservative. As a consequence, the solution is r…
Well-posedness of stochastic reacting particle systems with non-local and Lennard-Jones interactions
Daniela Morale, Giulia Rui, Stefania Ugolini
We establish well-posedness results for systems of a finite number of stochastic particles driven by independent Brownian motions and subject to a strongly singular drift induced b…
Path-dependent McKean PDEs with reaction: a discussion on probabilistic interpretations and particle approximations
Daniela Morale, Leonardo Tarquini, Stefania Ugolini
In this paper, we discuss and compare two probabilistic approaches for associating a stochastic differential equation with a McKean-type partial differential equation featuring a r…
Strong solutions to singular SDEs and application to the Lennard-Jones potential
Daniela Morale, Giulia Rui, Stefania Ugolini
We prove existence and uniqueness of strong solutions to a large class of autonomous stochastic differential equations on an open domain, where the drift exhibits a singular behavi…
Killed path-dependent McKean-Vlasov SDEs for a probabilistic representation of non-conservative McKean PDEs
Daniela Morale, Leonardo Tarquini, Stefania Ugolini
A McKean-Vlasov stochastic differential equation subject to killing associated to a regularised non-conservative and path-dependent nonlinear parabolic partial differential equatio…
Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results
Francesca Arceci, Francesco Carlo De Vecchi, Daniela Morale +1
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discret…